A generalization of the LLL-algorithm over Euclidean rings or orders

DOI10.5802/jtnb.176zbMath0876.11058OpenAlexW2071788187MaRDI QIDQ679101

Huguette Napias

Publication date: 26 November 1997

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_1996__8_2_387_0

zbMATH Keywords

Euclidean ringsLLL-algorithmlattice basis reductionlattices over ordersmaximal orders of imaginary quadratic fieldsorders of a quaternion algebra

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Algebraic number theory computations (11Y40)

Related Items (9)

The special case of cyclotomic fields in quantum algorithms for unit groups ⋮ Subfield algorithms for ideal- and module-SVP based on the decomposition group ⋮ Volumes and distributions for random unimodular complex and quaternion lattices ⋮ Short Stickelberger Class Relations and Application to Ideal-SVP ⋮ Short Bases of Lattices over Number Fields ⋮ On the reduction of a random basis ⋮ Fast reduction of algebraic lattices over cyclotomic fields ⋮ Lattice reduction for modules, or how to reduce ModuleSVP to ModuleSVP ⋮ Worst-case to average-case reductions for module lattices

Uses Software

• PARI/GP

Cites Work

• A modification of the LLL reduction algorithm
• Factoring polynomials with rational coefficients
• Applications of coding theory to the construction of modular lattices
• Neighborhood in the sense of Kneser for quaternionic lattices
• The Euclidean algorithm in algebraic number fields
• Structures algébriques sur les réseaux
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A generalization of the LLL-algorithm over Euclidean rings or orders